Results 151 to 160 of about 368,146 (227)

System of Ordinary Differential Equations

2009
In this chapter we focus on an autonomous system (Sect. 16.3), which is a specific type of system of ordinary differential equations. Autonomous systems can be used to describe the dynamics of the physical objects that are encountered in physics and engineering problems, wherein the laws governing the motion of the objects are time-independent, namely,
Hiroyuki Shima, Tsuneyoshi Nakayama
openaire   +2 more sources

Time-series forecasting using a system of ordinary differential equations

Information Sciences, 2011
Yuehui Chen, Bin Yang, Q. Meng, Ya-ou Zhao, A. Abraham   +4 more
semanticscholar   +3 more sources

The differential transform approximation for the system of ordinary differential equations

International Journal of Computer Mathematics, 2005
A. Kurnaz, G. Oturanç
semanticscholar   +3 more sources

The improved residual power series method for a system of differential equations: a new semi-numerical method

International Journal of Modelling and Simulation, 2023
This paper presents the extension of Improved Residual Power Series Method (IRPSM) towards the system of ordinary differential equations (ODEs). The present system of ODEs is based on the thin film flow over an inclined planar surface.
Abdullah Dawar, Hamid Khan, Saeed Islam, W. Khan   +3 more
semanticscholar   +1 more source

Ordinary Differential Equations

The Art of Modeling in Science and Engineering with Mathematica, 2021
The existing Neural ODE formulation relies on an explicit knowledge of the termination time. We extend Neural ODEs to implicitly defined termination criteria modeled by neural event functions, which can be chained together and differentiated through ...
Ricky T. Q. Chen, Brandon Amos, Maximilian Nickel   +2 more
semanticscholar   +1 more source

Multirate methods for ordinary differential equations

arXiv.org
This survey provides an overview of state-of-the art multirate schemes, which exploit the different time scales in the dynamics of a differential equation model by adapting the computational costs to different activity levels of the system.
Michael Günther, Adrian Sandu
semanticscholar   +1 more source

Systems of Ordinary Differential Equations

1988
In this chapter we discuss systems of first order ordinary differential equations and methods for their solutions. The importance of such systems stems from the following observations: 1. A coupled system of differential equations of any order can always be rewritten as a system of first order equations.
Mayer Humi, William Miller
openaire   +1 more source

PARTICULAR INTEGRALS OF SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS

Russian Academy of Sciences. Sbornik Mathematics, 1993
See the review in Zbl 0765.34007.
Gorbuzov, V. N., Tyshchenko, V. Yu.
openaire   +1 more source

Systems of Ordinary Differential Equations

2013
A system of ordinarydifferential equations (briefly, ODE’s) is a problem of finding functions \(y_{1}(x),\ldots,y_{n}(x)\) on some open interval in \(\mathbb{R}\) such that $$\displaystyle{ y_{k}\prime(x) = f_{k}(x,y_{1}(x),\ldots,y_{n}(x))\quad \text{for}\quad k = 1,\ldots,n }$$ (1.1.1) where f k are continuous functions of n + 1 real ...
Igor Kriz, Aleš Pultr
openaire   +1 more source